Can you please clarify what you mean by "understand what is going on"? Are they emitting only relative links, or rebasing the links to / instead of /app based on some information that's sent in the proxy request? Whether a web app will do that is going to be highly dependent on how it's built.
– Andrew SchulmanJan 4 '14 at 11:57

Both approaches are better than nothing, but the second one is more robust than simply outputting relative links. I understand that such behaviour is unreachable without using specific technologies (e.g.: MVC architecture with a single application entrypoint for every request), but hey, we are in 2014.
– Giovanni ToraldoJan 4 '14 at 12:01

Your web application at myip:8080/app probably has a lot of absolute paths in HTML and JS beginning with /app/... which cannot all be caught and rewritten by mod_proxy_html.

I would suggest to first try to get your app running at different local URLs like myip:8080/blah.
Fire up the developer toolbar of your browser and check the network tab for files that are still getting requested at /app/... and fix them until they work at both URLs (/blah and /app).

The goal should be that all your links in your app are relative, i.e. specified as

<script type="text/javascript" src="file.js"></script>

instead of something like this

<script type="text/javascript" src="/app/file.js"></script>

Also check out the <base> tag for a way to override the default base URL.